"As well" is used to include something. For example:
"Oh, you're going to see a movie? Can I come as well?"
"As well as sausages, the barbeque had burgers."
"I do enjoy vanilla ice cream, but I like strawberry as well."
"And" is also used for inclusion, but in different ways. For example:
"Oh, you're going to see a movie? Can you and I go together?"
"The barbeque had both sausages and burgers."
"I enjoy both vanilla and strawberry ice cream."